Sorry if I sound like a dick but that's complete bull**** that they would make you pay for a replacement battery when the original is bad and the phone is less than a week old. Insurance or not, you shouldn't have to pay for it. Also don't let them try to pass the buck and tell you to send it into Samsung. I would tell the agent that I understand it personally isn't their fault, but you would greatly appreciate it if they work with you on this and get you a swap out replacement at no charge. You don't want anything extra, just a new working battery to replace faulty one.
Wtf?! You've had the phone for less than a week and they made you PAY for a replacement? That's f'ed up! If the repair center wanted to charge you, I'd leave there, go back home and get all the **** that you got with the phone. Next I'd go back to the retail store and heavily suggest they give me a new replacement because this phone is not working correctly. If they give you grief then bluff them and tell them you want to return the phone (its still within the initial return period) and cancel your service because I'll be damned if I have to pay for a replacement part that was faulty and the phone is days old. You can also say that you'll report on the survey your story and give all failing marks.